Residual impurities in manganese (Mn) are a big obstacle to obtaining high-performance CdMnTe (CMT) X-ray and gamma-ray detectors. Generally, the zone-refining method is an effective way to improve the material's purity. In this work, we purified the MnTe compounds combining the zone-refining method with molten Te, which has a very high solubility for most impurities. We confirmed the improved purity of the material by glow-discharge mass spectrometry (GDMS). We also found that CMT crystals from a multiply-refined MnTe source, grown by the vertical Bridgman method, yielded better performing detectors.